Magnetics ..for JEE

Fill in the blanks:IIT-JEE pattern test-1 ( mag)-25 aug-12

1-A uniform magnetic field with a slit system as shown in figure, is to be used as a momentum filter for high energy charged particles. With a field B tesla, it is found that the filter transmits alpha particles each of energy 5.3 MeV. Themagnetic field is increased to 2.3 B tesla and deuterons are passed into the filter. The energy of each deuteron transmitted by the filter is ....Mev

2- An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +x direction and a magnetic field along the z-direction, then the positive ions deflect in …… direction and negative ion deflect in the ……..direction.

3-In a hydrogen atom, the electron moves in an orbit of radius 0.5 A making 1016 revolutions per seconds. The magnetic moment associated with the orbital motion of the electron is............

4-A wire ABCDEF (with each side of length L) bent as shown in the figure and carrying a current I is placed in a uniform magnetic induction B parallel to the positive y-direction The force experienced by the wire is ………in the . . . . direction

5-A wire of fength L metres carrying a current i amperes is bent in the form of a circle. The magnitude of its magnetic moment ..... in MKS unit.

6-The wire loop PQRSP formed by joining two semicircular wires of radii R1 and R2 carries a current I as shown. The magnitude of the magnetic induction at the centre C is ……………

7-A neutron, a proton, an electron and an alpha particle enter a region of constant magnetic field with equal velocities. The magnetic field is along the inward normal to the plane of the paper. The tracks of the particles are shown in the figure. The election follows track ……...and the alpha particle follows track ……………

TRUE/FALSE ( Q.Nos. 8,9,10,11)8-An electron and a proton are moving with the same kinetic energy along the same direction .When they pass through a uniform magnetic field perpendicular to the direction of their motions they describe circular paths of the same radius. 9- A charged particle enters a region of uniform magnetic field at an angle of 850 to the magnetic lines of the force. The path of the particle is a circle

10- There Is no change in the energy of a charged particle moving in a magnetic field although a magnetic force is acting on it.11- No net force acts on a rectangular coil carrying a steady current when suspended freely In a uniform magnetic field .

1 /magnetic/ IIT trends…

Choose single correct from the given four alternatives :

12-Which of the field patterns given below is valid for electric field as well as for magnetic field?

13-A wire is closely wound as a spiral Y of ‘N’ turns. The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the XY plane and a steady current flows through the wire.

The Z-component of the magnetic field at the centre of the spiral is.

14-A thin flexible wire of length L is connected to Iwo adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is (a)I B L (b) IBL/π (c) 0.5 IBL/π (d) 0.25 IBL/π

15- A magnetic field B = B0 j exists in the region a < x < 2a and B = —B0 j in the region 2a < x < 3a, where B is a positive constant. A positive point charge moving with a velocity = v0, where v0 is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,


16- An electron traveling with a speed u along the positive x-axis enters into a region of magnetic field where B = -B0 k (x> 0). It comes out of the region with speed v then (A) v=u at y > O (B ) v = u at y<0 (C) v>u at y>O (D) v>u at y<0

17-A positive charge moving along the positive x-direction with a speed v traces a non-linear trajectory OA in the x-y plane after passing O as shown in the figure. The combination of electric (E) and magnetic field B fields that would lead to the trajectory CA is (a, b, c are non-zero positive constants),

(A) E=0 ; B = ai+ck (B) E=a i ; B = bj+ck (C) E=0; B=b i+c k (D) E=ai; B = b i—ck

18- As shown in the figure, four identical loops are placed in a uniform magnetic field B. The loops carry equal current i. denotes the normal to the plane of each loop.

Potential energies in descending order are (a) I, II, III, IV (b) IV, II, III, I (c) I, III, II, IV (d) IV, III, II, I

19-

20- A long

straight wire along the z-axis carries a current I in the negative z direction. The magnetic vector field B at a point having coordinates (x, y) in the z = 0 plane is

21-A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending


from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is(A) qbB /m (B) q (b —a) B /m (C) aB q /m (D) q(b+a) B /(2m)

22- A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P(a 0, a) points

in the direction

23- Two particles A and B of masses mA and mB respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are VA and VB

respectively and the trajectories are as shown in the figure. Then (A) mA VA < mB VB (B) mAyA> mB V8 (C) mA < mB and VA<VB (D) mA=mB and vA = v8

24- An infinitely long conductor PQR is bent to form a right angle as shown in figure. A current I flows through PQR. The magnetic field due to the current at the point M is H1. Now, another infinitely long straight conductor QS is connected at Q so that current is I/2 in QR as well as in QS, the current in PQ remaining unchanged. The magnetic field at M is now H2. The ratio H1 / H2 (A) ½ (B) I (C) 2/3 (D) 2

25- Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper, as shown. The variation of the magnetic field B along the line XX’ is given by

26- A particle of charge +q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on (A) ω and q (B) q and m (C) q and m (D) ω and m

27- A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a (A) straight line (B) circle (C) helix (D) cycloid


28-Two particles, each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is (A) q /( 2m) (B) q/m (C) 2q/m (D) q/πm

29- A proton, a deuteron and an alpha particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and radenote respectively the radii of the trajectories of these particles, then (a)rα = rp < rd (b) rα > rd > rp (c) rα = rp > rd (d) rα = rp = rd

30- Two very long, straight, parallel wires carry steady currents I and - l respectively. The distance between the wires is d. At a certain instant of time, a point charge q is at a point equidistant from the two wires, in the plane of the wires. Its instantaneous velocity v is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is

(a) 0 I q v /( 2π d) (b) 0 I q v /( π d) (c) 0 2 I q v /( π d) (d) zero

31-A current I flows along the length of an infinitely long, straight, thin-walled pipe. Then (A) The magnetic field at all points inside the pipe is the same, but not zero (B) The magnetic field at any point inside the pipe is zero (C) The magnetic field is zero only on the axis of the pipe (D) he magnetic field is different at different points inside the pipe.

32-Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of the mass of X to that of Y is (A) (R1/ R2 )1/2 (B) R2/R1 (C) (R1/ R2 )2 (D) R1/ R2

33- Two thin long parallel wires separated by a distance ‘b’ are carrying a current I ampere each. The magnitude of the force per unit length exerted by one wire on the other is (A) 0 I /( 2π b ) (b) ) 0 I2 /( 2π b2 ) (c) ) 0 I2 /( 2π b ) (d) ) 0 I2 /( 4π b )

34-A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop, If steady current I is established in the wire as shown in the figure, the loop will(A) rotate about an axis parallel to the wire. (B) move away from the wire.

(C) move towards the wire. (D) remain stationary.

35-A conducting circular loop of radius R carries a constant current i. it is placed in a uniform magnetic field B such that B is perpendicular to the plane of the loop. The magnetic force acting on the loop is (A) I B R (B) 2 I B R (C) zero (D) 2π I B R


36-A magnetic needle is kept in a non-uniform magnetic field. It experiences (A) a force and a torque. (B) a force but not a torque. (C) a torque but not a force. (D) neither a force nor a torque.

37-Assertion-Reasoning STATEMENT-I The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil. and STATEMENT-2 Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

(A) STATEMENT-I is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-I (B) STATEMENT-l is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-I (C) STATEMENT -I is True, STATEMENT-2 is False (D) STATEMENT -I is False, STATEMENT-2 is True

38-An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is /are true? (A) They will never come out of the magnetic field region. (B) They will come out travelling along parallel paths. (C) They will come out after the same time interval (D) They will come out after different time interval

39-A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is l . Choose the correct choice(s).

Figure: (A) The particle enters region III only if its velocity V > qBl/m(B) The particle enters region Ill only if its velocity V < qBl/m (C) Path length of the particle in region II is maximum when velocity v = qBl/m(D) Time spent in region II is same for any velocity V as long as the particle returns to Region I .

40-A particle of charge +q and mass m moving under the influence of a uniform electric field E and uniform magnetic field B follows a trajectory from P to Q as shown in figure. The velocities at P and Q are v and - 2v which of the following statement (s) is/are correct? (A) E =3 m v2/ (4q a ) (B) Rate of work done by the electric field at P is 3 m v3/ (4 a ) (C) Rate of work done by the electric field at P is zero (D) Rate of work done both the fields at Q is zero


41-A proton moving with a constant velocity passes through a region of space without any change in its velocity. If E and B represent the electric and magnetic fields respectively, which of the following option(s) may be correct for this region of space (A) E=0, B=0 (B) E=0, B≠O (C) E≠ 0 ,B=0 (D) E≠0, B≠0

42-An infinite current carrying wire passes through point o and in perpendicular to the plane containing a current carrying loop ABCD as shown in the figure. Choose the correct option (s). (A) Net force on the loop, is zero. (B) Net torque on the loop is zero. (C) As seen from O, the loop rotates clockwise. (D) As seen from O, the loop rotates anti clockwise.

43-Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B the magnetic field at M and μ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

Column II Charges are at the corners of a regular hexagon. M is at the centre of the hexagon. PQ is perpendicular to the plane of the hexagon. Charges are on a line perpendicular to PQ at equal intervals. M is the mid-point between the two innermost charges. Charges are placed on two coplanar insulating rings at equal intervals. M is the common centre of the rings. PQ is perpendicular to the plane of the rings. Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. PQ is parallel to the longer sides. Charges are placed on two coplanar, identical insulating rings at equal intervals. M is the mid points between the centres of the rings. PQ is perpendicular to the line joining the centers and coplanar to the rings.

Column — I


(A). E =0 (B) V≠0(C) B =0(D) μ=≠

44-Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these statements to the appropriate system(s) from Column II.

Column II Block Y of mass M left on a fixed inclined plane X, slides on it with a constant velocity.

Two ring magnets Y and Z, each of mass M, are kept in frictionless vertical plastic stand so that they repel each other. Y rests on the base X and Z hangs in air in equilibrium. P is the topmost point of the stand on the common axis of the two rings. The whole system is in a lift that is going up with a constant velocity.


A pulley Y of mass m0 is fixed to a table through a clamp X. A block of mass M hangs from a string that goes over the pulley and is fixed at point P of the table. The whole system is kept in a lift that is going down with a constant velocity

A sphere Y of mass M is put in a nonviscous liquid X kept in a container at rest. The sphere is released and it moves down in the liquid.

A sphere Y of mass M is falling with its terminal velocity in a viscous liquid X kept in a container.

Column—I (A) The force exerted by X on Y has a magnitude Mg. (B) The gravitational potential energy of X is continuously increasing. (C) Mechanical energy of the system X + Y is continuously decreasing. (D) The torque of the weight of Y about point P is zero.

(p)

(q)


45-Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

(A) Point P is situated midway between the wires.

(B) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii.

(C) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii.

(D) Point P is situated at the common center of the wires.

Column II

(p) The magnetic fields (B) at P due to the currents in the wires are in the same direction.

(q) The magnetic fields (B) at P due to the currents in the wires are in opposite directions.

(r) There is no magnetic field at P.


(s) The wires repel each other.

Column I

46-A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k 0 I/( 48π x) find the value of k .

47- In a moving coil galvanometer, torque on the coil can be expressed as = ki, where i is current through the wire and k is constant. The rectangular coil of the galvanometer having number of turns N, area A and moment of inertia I is placed in magnetic field B. Find

(a) k in terms of given parameters N, I, A and B. (b) the torsion constant of the spring, if a current i0 produces a deflection of π/2 in the coil. (C) the maximum angle through which coil is deflected, if charge Q is passed through the coil almost instantaneously. (Ignore the damping in mechanical oscillations)

48-An α -partcle and a proton are accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature.

49-The axle of a circular wheel of radius R is held horizontally by two identical strings of equal lengths separated by a distance D. The tension in each string is T0. The rim of the wheel carries a total charge +Q distributed


uniformly on it. The wheel is vertical and is kept in a uniform vertical magnetic field B. It is now rotated at an angular speed ω If the string break at a tension of 3T0/2, calculate the maximum possible value of at which the wheel can be rotated without breaking a string.

50-A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field B = (3i + 4k)B0 exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium. (a) What is the direction of the current I in PQ? (b) Find the magnetic force on the arm RS. (C) Find the expression for I in terms of B0, a, b and m

51-A current of 10 A flows around a closed path in a circuit which is in the horizontal plane as shown in the figure. The circuit consists of eight alternating areas of radii r1= O.08 m and r2 = O.12 m. Each arc subtends the same angle at the centre. (a) Find the magnetic field produced by this circuit at the centre. (b) An infinitely long straight wire carrying a current of 10A is passing through the centre of the above circuit vertically with the direction of the current being into the plane of the circuit. What is the force acting on the wire at the centre due to the current in the circuit? What is the force acting on the arc AC and the straight segment CD due to the current at the centre?

52-A circular loop of radius R is bent along a diameter and given a shape as shown in the figure. One of the semicircles (KNM) lies in the x-z plane and the other one (KLM) in the y-z plane with their centres at the origin: Current I is flowing through each of the semicircles as shown in figure. (a) A particle of charge q is released at the origin with a velocity v = -v0j. Find the instantaneous force f on the particle. Assume that space is gravity free. (b) If an external uniform magnetic field Bj is applied determine the forces F1 and F2 on the semicircles KLM and KNM due to the field and the net force F on the loop.

53-The region between x = 0 and x = L is filled with uniform, steady magnetic field B0k. A particle of mass m, positive charge q and velocity v0 i travels along x-axis and enters the region of the magnetic field. Neglect gravity throughout the question.


(a) Find the value of L if the particle emerges from the region of magnetic field with its final velocity at angle 30° to its initial velocity. (b) Find the final velocity of the particle and the time spent by it in the magnetic field, if the magnetic field now extends up to 2.1 L.

54-A uniform constant magnetic field B is directed at an angle of 45° to the axis in the xy —plane. PQRS is a rigid, square wire frame carrying a steady current lo, with its centre at the origin 0. At time t = 0, the frame is at rest in the position as shown in figure, with its sides parallel to the x and y axes. Each side of the frame is of mass M and length L. (a) What is the torque t about O acting on the frame due to the magnetic field? (b) Find the angle by which the frame rotates under the action of this torque in a short interval of time t0, and the axis about which this rotation occurs. (t0 is so short that any variation in the torque during this interval may be neglected.) Given: the moment of inertia of the frame about an axis through its centre perpendicular to its plane is ML2/3.

55-A particle of mass m and charge q is moving in a region where uniform, constant electric and magnetic field E and B are present. E and B are parallel to each other. At time t =0 the velocity v0 of the particle is perpendicular to E. (Assume that its speed is always<<c, the speed of light in vacuum) Find the velocity of the particle at time t. You must answer in terms of t, q, m the vectors v0 E and B, and their magnitude v0, E and B.

56-Three infinitely long thin wires, each carrying current I in the same direction, are in the x-y plane of a gravity free space. The central wire is along the y-axis while the other two are along x= ±d. (a) Find the locus of the points for which the magnetic field B is zero. (b) If the central wire is displaced along the z-direction by a small amount and released, show that it will execute simple harmonic motion. If the linear density of the wires is ƛ, find the frequency of oscillation.

57-A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20 A, is in equilibrium at a height of 0.01 m over another parallel long wire CD, which is fixed in a horizontal plane and carries a steady current of 30 A, as shown in figure. Show that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations .

58-An electron gun G emits electrons of energy 2 keV travelling in the positive x-direction. The electrons are required to hit the spot S where GS = 0.1 m, and the line GS makes an angle 600 with the x - axis, as shown. A uniform magnetic field B parallel to GS exists in the region outside the electron gun. Find the minimum value of B needed to make the electrons hit S.

59-A straight segment CC (of length L metre) of a circuit carrying a current I amp is placed along the x-axis. Two infinitely long straight wires A & B, each extending from z= - to + are fixed at y = - a metre and y = +a


metre respectively, as shown in the figure. If the wires A and B each carry a current I amp into the plane of the paper, obtain the expression for the force acting on the segment CC. What will be the force on CC if the current in wire B is reversed?

60-A wire loop carrying a current i is placed in the x-y plane as shown in the figure. (a) If a particle with charge +Q and mass m is placed at the centre P and given a velocity along NP, find its instantaneous acceleration. (b) If an external uniform magnetic induction field B = B i is applied, find the force and torque acting on the loop due to this field.

61-Two long parallel wires carrying currents 2.5 A and I A in the same direction (directed into plane of the paper) are held at P and Q respectively such that they are perpendicular to the plane of paper. The points P and Q are located at a distance of 5 meters and 2 meters respectively from a collinear point R. (i) An electron moving with a velocity of 4 x 105 m/ s along the positive x-direction experiences a force of magnitude 3.2 x 10 - 20 N at the point R. Find the value of I.(ii) Find all the positions at which a third long parallel wire carrying a current of magnitude 2.5 amperes may be placed so that magnetic induction at R is zero.

62-A pair of stationary and infinitely long bent wires are placed in the XY plane as shown in the figure. The wires carry currents of I = 10 amp each as shown in the figure. The segments L and M are along the X axis. The segments P and Q are parallel to the Y-axis such that OS = OR = 0.02 m. Find the magnitude and direction of the magnetic induction at the origin O.

63-Two long straight parallel wires are 2 metres part, perpendicular to the plane of the paper. The wire A carries a current of 9.6 amps, directed into the plane of the paper. The wire B carries a current such that the magnetic field of induction at the point P, at a distance of 10/11 metre from the wire B, is zero. Find (i) The magnitude of direction of the current in B. (ii) The magnitude of the magnetic field of induction at the point S. (iii) The force per unit lQngth on the wire B.

64-A beam of protons with a velocity 4 x 105 m/s enters a uniform magnetic field of 0.3 tesla at an angle 600 to the magnetic field. Find the radius of the helical path taken by the proton beam. Also find the pitch of the helix (which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of


rotation).

65-A particle of mass m = 1.6 x 10 -27 kg and charge q = 1.6 x 1019 C enters a region of uniform magnetic field of strength 1 Tesla along the direction at E as shown in the figure. The speed of the particle is 107m/s. (I) The magnetic field is directed along the inward normal to the p[ane of the paper. The particle leaves the region of the field at the point F. Find the distance EF and the angle . (ii) If the direction of the field is along the outward normal to the plane of the paper, find the time spent by the particle in the region of the magnetic field after entering it at E.

66-A particle of mass I x 1026 kg and charge +1.6 x 1019C travelling with a velocity 1.28x106 m/s in the +x direction enters a region in which a uniform electric field E and a uniform magnetic field of induction B are present such that E= E = 0, E = —102.4 kVm-1 and Bx = Bz = 0. By = 8 x 10-2

Wbm-2. The particle enters this region at the origin at time t= 0. Determine the location (x, y and z coordinates) of the particle at t = 5 x 10 -6 s. If the electric field is switched of at this instant (with the magnetic field still present), what will be the position of the particle at t = 7.45 x I 0-6 s?


Documents

Magnetics ..for JEE